A. Sheikh Hosseini
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
[ 1 ] - Improvements of Young inequality using the Kantorovich constant
Some improvements of Young inequality and its reverse for positive numbers with Kantorovich constant $K(t, 2)=frac{(1+t)^2}{4t}$ are given. Using these inequalities some operator inequalities and Hilbert-Schmidt norm versions for matrices are proved. In particular, it is shown that if $a, b$ are positive numbers and $0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...
[ 2 ] - Some numerical radius inequalities with positive definite functions
Using several examples of positive definite functions, some inequalities for the numerical radius of matrices are investigated. Also, some open problems are stated.
[ 3 ] - Cartesian decomposition of matrices and some norm inequalities
Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements ...
[ 4 ] - Some weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
نویسندگان همکار